Question

Use the elimination method to solve the system of equations. Choose the correct ordered pair. x – 3y = –19 2x + y = –3

Answer 1

The given equations are,

$x-3y=-19$ and $2x+y=-3$

Multipying the second equation by 3 . we get,

$6x+3y=-9$

Now, If we add both the sides of both the equations. we get,

$x-3y+6x+3y=-28$

or

$7x = -28$

Which implies, $x=-4$

Substituting the value of x in any of the above equations. We get,

$y= 5$

Answer 2

The vertex is (-4,5). multiply the first equation by 2 and it will give you 2x-6y=-38. Then multiply the second equation by -1, and it will gives you -2x-y=3. cross off 2x and -2x, -6y-y=(-7y). -38+3=(-35). Now, you have -7y=-35, divide by -7, and you will get 5 for Y. Now to solve for X, all you have to do is to plug in the 5 to one of these equations. x-3(5)=-19, multiply the numbers -3x5=-15. x-15=-19, add 15 to both sides, you will get x=-4, and this is X. So the vertex is (-4,5) or X=-4 and Y=5.